Money doesn't work quite the same as it does on Earth. Firstly, there is no tangible currency; counterfeiting it is too trivial. Money is transfered usually by a person's tablet; to pay for something, you select the amount and tap your tablet against another tablet, the cash register, vending machine, or other similar device.
Secondly, money works in a fashion such that there is a concept of 'local money' and 'remote money'. Local money is money that you have transferred to your tablet. It's a bit like cash in a wallet, and this is how things are purchased when you are aboard the ship when it is underway and has no network access.
You can transfer that money to other local devices if desired, or transfer it around on the ship's local network. 'Remote money' is money that is in a bank account. It is only accessible when you have access to the galactic network. Access to the galactic network isn't reliable; there are plenty of places on the frontier that have no access, or network congestion can cause problems. It is usually wise, therefore, to keep some money local at all times and to mostly treat “remote money” as savings or emergency funds.
The exact way money works and is stored on devices is “magic”, in that “any sufficiently advanced technology is equivalent to magic” kind of way. As quantum computers are regularly available, standard blockchain style digital currencies wouldn't work. But it is a sufficiently complex system that it can't easily be counterfeited.
As an editor's note, I am loathe to assign “dollar figures” to things. Like, how much, exactly, does a starship cost? How much is a taco? How much is each crew member's paycheck? I'm not a numbers person, I don't enjoy delving into those details, and it is practically impossible to invent an economic system that isn't broken. It's not my strong suit, so I'm not going to try.
As such, I have described the crew pay as “good but not great”. Or maybe even “middle of the road”. However, on the Legacy, everyone gets free room and board. The only things crew have to pay for are certain items above and beyond normal food served by the ship's cooks.
Specifically, booze, name-brand sodas, and name-brand snacks (basically, vending machine items). If you get the snack from the food processor, it's free; if you pick something from the drink dispenser, it's free. But if you want, specifically, Space Oreos or Space Coke, you have to either buy it and bring it aboard or pay for it out of a vending machine.
Most corporate ships will nickle and dime crews; make them buy stuff from the company store, make them pay rent, and so forth. Thus, higher pay doesn't equal higher quality of life. Slightly less pay with practically all life expenses paid for is better than a bigger pay check and high cost of living.
Pay on the ship is issued at the end of each trip; so upon arrival at the next station or stop.
It is possible to own shares of the ship; shareholders, instead of getting paid a salary, are paid a proportional cut of the ship's profit after all expenses are accounted for. This is, generally speaking, more money than could be made with a regular salary.
The catch is, there is no desire for investors that aren't a part of the ship. Therefore, only people committed to staying with the ship are allowed to buy shares. If, at some point, a shareholder decides to leave, they must sell their shares back to the ship as part of the ownership contract.
Thus, only people that have chosen to settle and make a family are likely to be offered the option to purchase shares.
Share price is determined by an automatic calculation based on the past year's worth of revenue. They are “expensive”, whatever that means; probably about the equivalent of purchasing a new car. However, the return rate is high so it is worth the investment.
Current shareholders, in order of ownership: